This happens all the time in Texas. A warrant can be issued at any time by magistrate, providing probable cause exists to believe that you have committed a crime. Lack of knowledge of the existence of the warrant does not vitiate its viability. You need to hire a good lawyer immediately.
No, an arrest warrant can be executed against you anywhere you are found.
Think of it this way. If the police had to give every criminal notice he was about to be arrested before the actual arrest, there would be lots more attempt to avoid arrest and far fewer criminal in custody. So, as a society we are well served in allowing the police to do their job.
The police don't need to notify you when there is a warrant out for your arrest. If they did that, then many people would flee to avoid arrest. If you feel the warrant was issued improperly, you should consult with a criminal defense attorney who will be able to determine if that is the case.
THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.